What historic reasons are there for common aspect ratios?

Question

The most common width to height ratio rates in the "old good" paper photography seems to be 3:2, which was adopted by today's DSLRs. Early (non-professional) digital cameras adopted 4:3 aspect ratio, which was the industry standard for computer monitors and for consumer TV sets. Prints are often 5:4 (as in 4"x5" or 8"x10"). Wide-format monitors are 16:9. Does anyone have any idea where and why these aspect ratio conventions were adopted in the first place?

Answer

Some common formats and a bit about their history:

4:3

This was the aspect ratio chosen as the standard for for silent film. Adding room for the soundtrack changed the standard slightly, but it's still the foundation. That translated to television sets, and then to computer monitors, and therefore was a natural choice for early digital cameras, and of course continues to today.

Somewhat ironically, wider formats came to cinema largely as a way to distinguish the awesomeness of theaters from home viewing. See this for more, or search for "Academy ratio" and you'll get lots of information.

3:2

This is the format of 35mm film and the de facto standard for digital SLRs. Oskar Barnack of Leitz invented a small camera using cinema film rolls, and chose to use a double frame — and a double 4:3 frame is 4:6 — which is to say, 3:2 when you turn it 90°. This is the origin of the 35mm film format, and here we are today.

(Beware when searching for more on this; there's an oft-repeated article out there full of unwarranted golden-ratio mysticism.)

When the Advanced Photo System standard was invented, "APS-C" was defined to follow this Classic aspect ratio (in a smaller size). APS also defined APS-P (a 3:1 panorama), which didn't really catch on; and APS-H, which is close to but not exactly 16:9 (but probably chosen for its similarity).

1:1

Squares are obvious, and nice to compose in. There's no concern about "portrait" or "landscape" orientation. Interestingly, analysis of historically-preferred aspect ratio in painting show that with no inherent restrictions of format, artists tended towards more square.

5:4

This is a common large format aspect ratio. I'm not sure why exactly it was chosen, but I wouldn't be surprised it simply fits with the historical preferences for almost-square frames as noted above. The popular 8"×10" print fits this format.

I imagine the history here roughly mirrors the history of standardized sizes for letter paper.

6:7

This is a relatively-common medium-format aspect ratio, and as I understand it, was historically chosen as a conveniently-close-to-8×10-for-printing way of dividing up a roll of medium-format film.

16:9

This is the standard for HDTV, of course, and it was simply selected as a compromise format by the committee designing that standard. Hooray for committees! This forum thread goes into the background of the decision, but really, committee compromise sums it up.

Check more discussion of this question.